Rayleigh Criterion (thermo-acoustic Instability)

Thermo-acoustic instability refers to an instabiltiy arising due to acoustics field and unsteady heat release process. This instability is very relevant in combustion instabilities in systems such as rocket engines, etc.Williams, F. A. (2018). Combustion theory. CRC Press.

Rayleigh criterion

A very simple mechanism of acoustic amplification was first identified by Lord Rayleigh in 1878.Rayleigh, J. W. S. B. (1896). The theory of sound (Vol. 2). Macmillan. In simple terms, Rayleigh criterion states that ''amplification results if, on the average, heat addition occurs in phase with the pressure increases during the oscillation''.. That is, if $p'$ is the pressure perturbation (with respect to its mean value $\langle p\rangle$) and $\dot q'$ is the rate of heat release per unit volume (with respect to its mean value $\langle \dot q\rangle$), then the Rayleigh criterion says that acoustic amplification occurs if

$\langle p' \dot q' \rangle >0.$

Rayleigh criterion is used to many explain phenomena such as singing flames in tubes, sound amplification in Rijke tube and others. In complex systems, Rayleigh criterion, may not be strictly valid, as there exists many damping factors such as viscous/wall/nozzle/relaxation/homogeneous/particle damping, mean-flow effects, et, that are not accounted in Rayleigh's analysis.

See also

*Darrieus–Landau instability
* Diffusive–thermal instability
* Rijke tube

References

{{DEFAULTSORT:Thermo-acoustic instability
Fluid dynamics
Combustion
Fluid dynamic instabilities